A reconciliation of the Pryce-Ward and Klein-Nishina statistics for semi-classical simulations of annihilation photons correlations

TL;DR

This paper addresses the challenge of reconciling two different statistical descriptions of entangled photon scattering in semi-classical simulations, proposing a modified cross section to unify the models.

Contribution

It introduces a modified scattering cross section that bridges Pryce-Ward and Klein-Nishina descriptions for semi-classical simulations of entangled photon interactions.

Findings

Reconciliation of Pryce-Ward and Klein-Nishina models achieved

Modified cross section enables consistent semi-classical simulations

Enhanced understanding of photon entanglement effects in scattering

Abstract

Two photons from the ground state para-positronium annihilation are emitted in a maximally entangled singlet state of orthogonal polarizations. In case of the Compton scattering of both photons the phenomenon of quantum entanglement leads to a measurable increase in the azimuthal correlations of scattered photons, as opposed to a classical description treating the two scattering events as independent. The probability of the scattering of the system of the entangled photons is described by the Pryce-Ward cross section dependent on a difference of the azimuthal scattering angles in the fixed coordinate frame, while the independent scattering of single photons is described by the Klein-Nishina cross section dependent on the azimuthal angle relative to each photon's initial polarization. Since the singlet state of orthogonal polarizations is rotationally invariant, it does not carry any physical information on the initial polarizations of the single annihilation photons. In such bipartite state the angular origin for the Klein-Nishina cross section is undefined, making the Pryce-Ward and Klein-Nishina descriptions mutually exclusive. However, semi-classical simulations of the joint Compton scattering of entangled photons - implementing the Pryce-Ward cross section, but still treating the two photons as separate entities - can reconcile the Pryce-Ward correlations with the Klein-Nishina statistics for single photons by implementing a modified version of a scattering cross section presented in this work.